Economic Model Predictive Control for Closed-Loop Chemical Reactor Scheduling

 

Abstract

Traditionally, scheduling and control are viewed as two related but disparate engineering activities.  For scheduling, the main decisions are typically discrete yes/no choices; the models capture only important discrete events and transitions but include many units; and, the objective is generally economic in some sense (minimize, e.g., cost or earliness).  For control, the decisions are almost always continuous in nature; the models describe detailed temporal dynamics of the system but are local in scope; and, the objective function is artificially designed to maintain the system at a predetermined setpoint.  Despite these differences, both problems can be addressed by formulating a mathematical optimization and solving it repeatedly as new information is received.  For control systems, re-optimization is necessary to compensate for unknown disturbances and model errors, or to respond to changes in setpoint, and these same general considerations also trigger rescheduling.  While the timescales may be quite different (in terms of both the horizon of optimization and how frequently optimization is performed), this similarity raises the question of whether the two disciplines can be unified under a single mathematical treatment.  In this presentation, we advance the idea that certain classes of scheduling and control problems are indeed two variants of the same overall problem that differ only in their respective system dynamics and decision space, and thus can be analyzed using a common set of tools.

 

To exploit this connection, we revisit previous work that shows how a common scheduling model can be written in state-space form.  This abstraction allows the model to be viewed as a dynamic system rather than as a set of combinatorial constraints.  Next, we discuss results showing that, with suitable assumptions, the presence of discrete-valued control inputs does not affect the stability properties of model predictive control (MPC).  Combining these ideas, we show that economically optimizing scheduling and control problems can both be viewed as cases of dynamic real-time optimization or economic MPC, which has important ramifications for closed-loop implementation.  These connections are illustrated throughout the talk with simple, easy-to-understand chemical production scheduling problems.

 

• Election to the National Academy of Engineering
• William H. Walker Award for Excellence in Contributions to Chemical Engineering Literature from the AIChE
• "Doctor technices honoris causa" from the Danish Technical University
• The inaugural High Impact Paper Award from the International Federation of Automatic Control
• The Ragazzini Education Award from the American Automatic Control Council
• The Computing in Chemical Engineering Award and Excellence in Process Development Award from the AICHE
• The Chancellor's Distinguished Teaching Award, a WARF Named Professorship, and the Byron Bird Award for Excellence in a Research Publication, from the University of Wisconsin
• He is a fellow of IFAC, IEEE, and AIChE